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2 years ago

Joshua invested $750 in an account paying an interest rate of

1 answer:

5 0

Due to the difference in the interest rate and the quarterly compounding, Joshua will have $212.24 more than Josiah.
Step-by-step explanation:
Giving the following information:
Joshua:
Initial investment (PV)= $750
Interest rate (i)= 0.0341/4= 0.008525
Number of periods (n)= 18*4= 72 quarters
Josiah:
Initial investment (PV)= $750
Interest rate (i)= 0.0285
Number of periods (n)= 18 years
To calculate the future value of each one, we need to use the following formula:
FV= PV*(1 + i)^n
Joshua:
FV= 750*(1.008525^72)
FV= $1,381.98
Josiah:
FV= 750*(1.0285^18)
FV= $1,169.74
Due to the difference in the interest rate and the quarterly compounding, Joshua will have $212.24 more than Josiah.

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Solve the Anti derivative.

Alex Ar [27]

Answer:

$\displaystyle \int {\frac{1}{9x^2+4}} \, dx = \frac{1}{6}arctan(\frac{3x}{2}) + C$

General Formulas and Concepts:

Algebra I

Factoring

Calculus

Antiderivatives - integrals/Integration

Integration Constant C

U-Substitution

Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

Trig Integration: $\displaystyle \int {\frac{du}{a^2 + u^2}} = \frac{1}{a}arctan(\frac{u}{a}) + C$

Step-by-step explanation:

Step 1: Define

$\displaystyle \int {\frac{1}{9x^2 + 4}} \, dx$

Step 2: Integrate Pt. 1

[Integral] Factor fraction denominator: $\displaystyle \int {\frac{1}{9(x^2 + \frac{4}{9})}} \, dx$
[Integral] Integration Property - Multiplied Constant: $\displaystyle \frac{1}{9} \int {\frac{1}{x^2 + \frac{4}{9}}} \, dx$

Step 3: Identify Variables

Set up u-substitution for the arctan trig integration.

$\displaystyle u = x \\ a = \frac{2}{3} \\ du = dx$

Step 4: Integrate Pt. 2

[Integral] Substitute u-du: $\displaystyle \frac{1}{9} \int {\frac{1}{u^2 + (\frac{2}{3})^2} \, du$
[Integral] Trig Integration: $\displaystyle \frac{1}{9}[\frac{1}{\frac{2}{3}}arctan(\frac{u}{\frac{2}{3}})] + C$
[Integral] Simplify: $\displaystyle \frac{1}{9}[\frac{3}{2}arctan(\frac{3u}{2})] + C$
[integral] Multiply: $\displaystyle \frac{1}{6}arctan(\frac{3u}{2}) + C$
[Integral] Back-Substitute: $\displaystyle \frac{1}{6}arctan(\frac{3x}{2}) + C$

Topic: AP Calculus AB

Unit: Integrals - Arctrig

Book: College Calculus 10e

7 0

3 years ago

Riley has collected surveys for her final thesis project. One one question, 46.1% of respondents said that conditions were impro

ira [324]

Answer:

The maximum value of the confidence interval for this set of survey results is 51.73%.

Step-by-step explanation:

A confidence interval has two bounds, a lower bound and an upper bound.

These bounds depend on the sample proportion and on the margin of error.

The lower bound is the sample proportion subtracted by the margin of error.

The upper bound is the margin of error added to the sample proportion.

In this question:

Sample proportion: 46.1%

Margin of error: 5.63%.

Maximum value is the upper bound:

46.1+5.63 = 51.73

The maximum value of the confidence interval for this set of survey results is 51.73%.

5 0

4 years ago

Find the total area of the entire figure. *

bonufazy [111]

Answer:

392.5 in²

Step-by-step explanation:

This figure is consists of a trapezium and a rectangle.

So, to find the total area of the figure you have to find the area of the trapezium and the rectangle separately and add them together.

Let us find now.

Area of the Trapezium

Area = $\frac{1}{2}$ × ( sum of the parallel sides ) × height

Area = $\frac{1}{2}$ × ( 9 + 20 ) × 5

Area = $\frac{1}{2}$ × 29 × 5

Area = $\frac{1}{2}$ × 145

Area = 72.5 in²

Area of the rectangle

Area = Length × Width

Area = 20 × 16

Area = 320 in²

Total area of the figure

Total area = Area of the trapezium + Area of the rectangle

Total area = 72.5 in² + 320 in²

Total area = 392.5 in²

Hope this helps you :-)

Let me know if you have any other questions :-)

6 0

2 years ago

How do you solve k/2+9=30

Mrrafil [7]

If you would like to solve the equation k / 2 + 9 = 30, you can calculate this using the following steps:

k / 2 + 9 = 30
k / 2 = 30 - 9
k / 2 = 21 /*2
k = 21 * 2
k = 42

The result is 42.

4 0

3 years ago

Read 2 more answers

It is 17 miles to the mall how many inches is that on a map

Alona [7]

In order to answer that question, we need to know the scale of the map.
Without that information, no answer is possible.

I think you have it in the first part of the question ... the part you decided
not to post.
_________________________

OK. Now that you've provided the scale of the map,
answering the question is a piece-o-cake.
Use a proportion:

(1 inch on the map) / (4 miles on the ground) = ('x' on the map) / (17 miles on the ground)

3 0

3 years ago